The present invention relates generally to communication systems, and more particularly to time-domain equalization of a communication channel.
FIG. 1 shows a typical communication system 100 having a local/central unit 102 in communication with a remote unit 106 over a communication medium 104. Generally speaking, the communication medium 104 supports bi-directional communications between the local/central unit 102 and the remote unit 106. For convenience, communications from the local/central unit 102 to the remote unit 106 are said to be xe2x80x9cdownstreamxe2x80x9d communications, while communications from the remote unit 106 to the local/central unit 102 are said to be xe2x80x9cupstreamxe2x80x9d communications. Thus, the communication medium 104 typically supports a downstream channel over which the local/central unit 102 communicates to the remote unit 106 and an upstream channel over which the remote unit 106 communicates to the local/central unit 102. The upstream channel and the downstream channel may share the same physical communication link or occupy different physical communication links. When the upstream channel and the downstream channel share the same physical communication link, the upstream channel and the downstream channel may occupy the same frequency band (e.g., analog modem channels) or different, typically non-overlapping, frequency bands (e.g., ADSL or cable modem channels). The upstream and downstream channels may be symmetric or asymmetric.
Within the communication system 100, it is common for the upstream and downstream communication channels to have dispersive characteristics. Specifically, each channel has a particular impulse response that disperses signals carried over the channel by extending the effects of each signal over a period of time. In many cases, the dispersive nature of the channel causes various distortions of the signals carried over the channel, such as Inter-Symbol Interference (ISI), Inter-Carrier Interference (ICI), and other distortions.
FIG. 2A shows a representation of an exemplary transmit signal 210 that is transmitted over a dispersive channel, for example, by the local/central unit 102. The exemplary transmit signal 210 includes two symbols, S1 (211) and S2 (212), that are transmitted over the dispersive channel with no inter-symbol delay.
FIG. 2B shows a representation of an exemplary receive signal 220 that is received over the dispersive channel, for example, by the remote unit 106, when the symbols S1 (211) and S2 (212) are transmitted over the dispersive channel with no inter-symbol delay. As shown in FIG. 2B, the transmitted symbol S1 (211) is dispersed by the dispersive channel such that the received symbol R1 (221) overlaps the beginning of the symbol S2 (212). This causes ISI between the symbols S1 (211) and S2 (212) and therefore corruption of the symbol S2 (212).
One way to avoid or reduce ISI is to add a sufficient amount of inter-symbol delay to the transmitted symbols so that the received symbols do not overlap.
FIG. 3A shows a representation of an exemplary transmit signal 310 that is transmitted over a dispersive channel, for example, by the local/central unit 102. The exemplary transmit signal 310 includes two symbols, S1 (311) and S2 (312), that are transmitted over the dispersive channel with inter-symbol delay.
FIG. 3B shows a representation of an exemplary receive signal 320 that is received over the dispersive channel, for example, by the remote unit 106, when the symbols S1 (311) and S2 (312) are transmitted over the dispersive channel with inter-symbol delay. As shown in FIG. 3B, the transmitted symbols S1 (311) and S2 (312) are dispersed by the dispersive channel. However, because of the inter-symbol delay in the transmitted signal, the received symbols R1 (321) and R2 (322) do not overlap. As a result, there is no ISI between the symbols S1 (311) and S2 (312).
While the inter-symbol delay added to the transmitted signal eliminates (or at least reduces) ISI, there are detriments to employing such inter-symbol delay. For one, the inter-symbol delay reduces the efficiency of the transmitted signal in that fewer symbols (and therefore less data) are transmitted over a particular period of time. Also, the inter-symbol delay can cause cross-talk between channels carried over a common physical communication link. Thus, inter-symbol delay may be impractical for certain applications.
Another way to avoid or reduce ISI is to xe2x80x9cshortenxe2x80x9d the impulse response of the channel. This is typically done using a time-domain equalizer (TEQ) at the receiving end of the communication channel. The TEQ is a short Finite Impulse Response (FIR) filter that is used to time-compress (shorten) the impulse response of the communication channel. In addition to shortening the impulse response of the channel, the TEQ also tends to xe2x80x9cflattenxe2x80x9d the channel and amplify noise. The effectiveness of the TEQ has a direct impact on overall performance, and therefore the TEQ design and the TEQ coefficients must be carefully determined. There are typically different design considerations for time-domain equalization of the upstream and downstream channels. Also, whether the implementation platform is memory or processing power limited (or both) plays an important role in the TEQ design.
The following references are hereby incorporated herein by reference in their entireties, and may be referenced throughout the specification using the corresponding reference number. It should be noted that the reference numbers are not consecutive.
[1] John A. C. Bingham, ADSL, VDSL and Multicarrier Modulation, John Wiley and Sons, 2000.
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[3] D. D. Falconer and F. R. Magee, Jr., xe2x80x9cAdaptive Channel Memory Truncation for maximum Likelihood Sequence Estimator,xe2x80x9d B.S.T.J. November 1973, pp. 1541-1562.
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In accordance with an aspect of the invention, a technique for time-domain equalizer (TEQ) training determines the TEQ order and TEQ coefficients by applying the multichannel Levinson algorithm for auto-regressive moving average (ARMA) modeling of the channel impulse response. Specifically, the TEQ is trained based upon a received training signal. The received training signal and knowledge of the transmitted training signal are used to derive an autocorrelation matrix that is used in formulating the multichannel ARMA model. The parameters of the multichannel ARMA model are estimated via a recursive procedure using the multichannel Levinson algorithm. Starting from a sufficiently high-order model with a fixed pole-zero difference, the TEQ coefficients corresponding to a low-order model are derived from those of a high-order model. For each set of TEQ coefficients, a shortened signal to noise ratio (SSNR) or other performance-measuring statistic is calculated from the output sequence of the TEQ. The set of coefficients providing the best performance (and hence the highest throughput) are selected for the TEQ. Because the recursive procedure can become unstable due to computational errors caused by exceeding the computational precision of the underlying architecture, a stability indicator is monitored during the recursions in order to detect instability and terminate the recursions thereupon.